Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#5240 | C2 | semidirect |
| 3. C5×#4545 | C2 | semidirect |
| 6. C22×C3×C5×D4 | C4 | semidirect |
| 8. C3×C5×#124 | C4 | semidirect |
| 11. C3×C5×#117 | C4 | semidirect |
| 14. C5×#834 | C22 | semidirect |
| 15. #71861 | C5 | direct (N × H) |
| 38. #5240 | C2×C5 | semidirect |
| 39. #4545 | C2×C5 | semidirect |
| 41. C22×C5×D4 | Dic3 | semidirect |
| 43. C5×#124 | Dic3 | semidirect |
| 47. C5×#117 | Dic3 | semidirect |
| 71. C22×C3×D4 | C4×C5 | semidirect |
| 73. C3×#124 | C4×C5 | semidirect |
| 76. C3×#117 | C4×C5 | semidirect |
| 79. #834 | C22×C5 | semidirect |
| 152. C22×D4 | C5×Dic3 | semidirect |
| 154. #124 | C5×Dic3 | semidirect |
| 158. #117 | C5×Dic3 | semidirect |
| 216. C3×C5 | #2128 | semidirect |
| 259. C5 | #71861 | direct (N × H) |
| 273. C3 | C5×#2128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#535 | 2 |
| C5×#5240 | 2 |
| C5×#4545 | 2 |
| C5×#2128 | 3 |
| #71861 | 5 |